Interactive Infinite Limits and Limits at Infinity by Renata

This GeoGebra applet interactively demonstrates infinite limits and limits at infinity by dragging the red point along the x-axis to show how the output behaves as inputs grow without bound (or move toward infinity). It focuses on core calculus ideas: “infinite limits” (diverging toward ±∞) and “limits at infinity” (the limiting behavior as x → ±∞), linking the numeric behavior to the visual geometry in the graph. The construction uses GeoGebra commands such as Point, Polygon, and Vector to build multiple key points (e.g., H, K, L, M, N and related points k, l, m, n), assemble polygonal/connected shapes (poly1) for the visualization framework, and employ vector/arrow-like objects (e.g., g, u, v) to guide interpretation; text labels (text1) help annotate what is being shown. Parameter and function variables (f, a, b, A, B, plus c–e and h–i style parameters) drive the dynamic behavior. Suitable for secondary-school advanced calculus introductions, early university calculus, classroom demonstrations, and self-study of limit concepts through visual reasoning.